A new convergent algorithm to approximate potentials from fixed angle scattering data

TL;DR

This paper presents a novel iterative algorithm that reconstructs potentials in Schrödinger operators from fixed angle scattering data, combining fixed point methods with Born series approximations, and demonstrates convergence through numerical experiments.

Contribution

It introduces a new convergent iterative method for potential recovery from fixed angle scattering data, integrating fixed point theory with Born series approximations.

Findings

Convergence proven for small norm potentials in Sobolev spaces

Numerical experiments confirm the effectiveness of the method

Method successfully reconstructs potentials from scattering data

Abstract

We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the resolvent of the Schr\"odinger operator by partial sums associated to its Born series. Convergence is established for potentials with small norm in certain Sobolev spaces. As an application we show some numerical experiments that illustrate this convergence.